\(T_5\)-configurations and non-rigid sets of matrices
type: Item
instance of: scholarly article
title: \(T_5\)-configurations and non-rigid sets of matrices
zbMATH Open document ID: 1414.34015
author: Clemens Förster
author: László jun. Székelyhidi
published in: Calculus of Variations and Partial Differential Equations
publication date: 2018-03-01T00:00:00Z
review text: Based on the notion of \(T_{N}\)-configuration (already used for \(N=4\) in the context of differential inclusions by \textit{S. Müller} and \textit{V. Šverák} [Ann. Math. (2) 157, No. 3, 715--742 (2003; Zbl 1083.35032)]), the authors introduce the notion of large \(T_{5}\)-set. The main result in the paper states that if a \(5\) element set \(K\) of \(2\times 2\) matrices is a large \(T_{5}\)-set, then it is non-rigid, that is, the differential inclusion \(Du(x)\in K,\) \(x\in \Omega \) (with \(\Omega \) being a bounded domain with Lipschitz boundary) admits non-affine Lipschitz solutions.
Mathematics Subject Classification ID: 34A60
Mathematics Subject Classification ID: 49K21
Mathematics Subject Classification ID: 26B25
zbMATH DE Number: 6845936
zbMATH Keywords: differential inclusions
zbMATH Keywords: convex integration
zbMATH Keywords: rank-one convexity
reviewed by: Juan-Enrique Martínez-Legaz
MaRDI profile type: Publication
full work available at URL: s00526-017-1293-7
OpenAlex ID: W2776165254
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DOI: 10.1007/S00526-017-1293-7
description: scientific article; zbMATH DE number 6845936